Simplify the following expression: $\dfrac{55r^2}{132r^4}$ You can assume $r \neq 0$.
Solution: $ \dfrac{55r^2}{132r^4} = \dfrac{55}{132} \cdot \dfrac{r^2}{r^4} $ To simplify $\frac{55}{132}$ , find the greatest common factor (GCD) of $55$ and $132$ $55 = 5 \cdot 11$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(55, 132) = 11 $ $ \dfrac{55}{132} \cdot \dfrac{r^2}{r^4} = \dfrac{11 \cdot 5}{11 \cdot 12} \cdot \dfrac{r^2}{r^4} $ $\phantom{ \dfrac{55}{132} \cdot \dfrac{2}{4}} = \dfrac{5}{12} \cdot \dfrac{r^2}{r^4} $ $ \dfrac{r^2}{r^4} = \dfrac{r \cdot r}{r \cdot r \cdot r \cdot r} = \dfrac{1}{r^2} $ $ \dfrac{5}{12} \cdot \dfrac{1}{r^2} = \dfrac{5}{12r^2} $